Question

find rate percent is rupees 2000 amounts to rupees 2662 in one and half years interest being compounded half yearly. ​

Answer 1

Half yearly means timw double ,3/2×2=3 yr

2662/2000=(1+r/100)^3

1331/1000=(1+r/100)^3

11/10=1 + r/100

1/10=r/100

r=10%

hope this helps you

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Answer 2

$\mathfrak{Step-By-Step\;Explanation:}$

Given :

• Principle = Rs.2000.

• Time = one and half years.

• Amount = Rs.2662.

Let the rate of interest be r % .

We know that if interest is compounded half yearly then ,

$\boxed{\bold{Amount=Principle\left(1+\dfrac{r}{200}\right)^{2n}}}\\\\\\\implies\bold{2662=2000\left(1+\dfrac{r}{200}\right)^{2\times \frac{3}{2}}}\\\\\\\implies\bold{\dfrac{2662}{2000}=\left(1+\dfrac{r}{200}\right)^3}\\\\\\\implies\bold{\dfrac{1331}{1000}=\left(1+\dfrac{r}{200}\right)^3}\\\\\\\implies\bold{\left(\dfrac{11}{10}\right)^3=\left(1+\dfrac{r}{200}\right)^3}\\\\\\\implies\bold{\dfrac{11}{10}=\dfrac{200+r}{200}}\\\\\\\implies\bold{\dfrac{11\times 200}{10}=200+r}$

$\implies\bold{220=200+r}\\\\\\\implies\bold{r=220-200}\\\\\\\therefore\quad \tt{r=20\%.}\\\\\\\\\boxed{\boxed{\bold{Rate=20\%.}}}$